Journal o f t h e American Chemical Societj$ 1 I02:3
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(Trasylol) and Shell Development Co., Houston. Texas, for the use of their 90-MHz "C Y M R facilities. We especially wish to thank Ms.Ruth lnners for obtaining initial spectra at 25 and 90 MHz and Dr. Dale Holecek of Shell Development for his assistance in obtaining the 90-MHz spectra.
References and Notes (1) Abbreviations used: '3C NMR. 13C nuclear magnetic resonance; BPTI, basic pancreatic trypsin inhibitor (bovine): SM-BPTI, [ S-['3C]methyl methionine-52l-BPTI; ppm, parts per million: Z, benzyloxycarbonyl. (2) W. C. Jones. Jr., T. M. Rothgeb, and F. R. N. Gurd, J. Am. Chem. Soc., 97, 3875 (1975). (3) W. C. Jones, Jr., T. M. Rothgeb, and F. R. N. Gurd, J. Biol. Chem., 251, 7452 ( 1976). (4) C. M. Deber, M. A. Moscarello, and D. P. Wood, Biochemistry, 17, 898 (1978). (5) T. M. Rothgeb, 6.N. Jones, D. F. Hayes and R. S . Gurd, Biochemistry, 16, 5813 (1977). (6) R. Huber. D. Kukla, A. Ruhlmann, 0. Epp, and H. Formanek, Naturwissenschaften, 57, 389 (1970). (7) B. M. Harina, D. F. Dyckes, M. R. Willcott, 111, and W. C. Jones, Jr., J. Am. Chem. SOC.. 100, 4897 (1978). (8) J. A. Moore and D. L. Dalrymple in "Experimental Methods in Organic Chemistry", W. B. Saunders, Philadelphia, 1976, p 255.
/ January 30, I980
(9) K . Hofmann, A. Johl. A. E. Furlenmeier, and H. Kappeler. J. Am. Chem. Soc., 79, 1636 (1957). (IO) D. F. Dyckes, T. E. Creighton, and R. C. Sheppard, Nature (London), 247, 202 (1974). (1 1) D. F. Dyckes, T. E. Creighton, and R. C. Sheppard. Int. J. Pept Protein Res., 11, 258 (1978). (12) E. Kassell, Methods Enzymol.. 19, 844 (1970). (13) A 0.06-ppm separation in the C-13 methyl signals of Z-SM-Met at 25 MHz has been observed r e ~ e n t l yThe . ~ pH was not reported. (14) The methyl ester of ['3C]-SM-methionine at pH 10 exhibited a 0.9-Hz separation in the S-methyl signals at 90 MHz. Under these conditions the corresponding signal for [ 13C]-SM-methionineamide showed an unresolved shoulder on the upfield side. (15) The carboxymethylated SM protein was observed at low pH for reasons of solubility. The heatdenatured SM protein remains soluble at physiological PH. (16) M. P. Sherman and 6.Kassell, Biochemistry, 7, 3634 (1968). (17) E. Sach, M. Thely, and J. Choay. C. R. Acad. Sci., 260, 3491 (1965). (18) N. M. Green and E. Work, Biochem. J., 54, 257 (1953). (19) M. Kunitz and J. H. Northrop. J. Gen. Physiol., 19, 991 (1936). (20) S. Karplus, G. H. Snyder, and B. D. Sykes, Biochemistry, 12, 1323 (1973). (21) A. Masson and K. Wutrhrich, FEBSLett., 31, 114 (1973). (22) 6.Kassell. Biochemistry, 3, 152 (1964). (23) T. E. Creighton, D. F. Dyckes, and R. C. Sheppard, J. Mol. Biol., 119, 507 (1978). (24) D. F. Dyckes and T. E. Creighton, manuscript in preparation
23Na,and 31PNMR Studies of the Self-Assembly of the 5'-Guanosine Monophosphate Dianion in Neutral Aqueous Solution in the Presence of Sodium Cations lH,
Marie Borzo, Christian Detellier, Pierre Laszlo," and Agnes Paris Contributionfrom the Institut de Chimie Organique et de Biochiniie ( B 6 ) , Unirersith de LiZge, Sart-Tilman par 4000 LiPge. Belgium. Receiced April 12, 1979
Abstract: [ H chemical shifts show at concentrations below 0.2 M a normal stacking process, with an apparent mean equilibrium constant of 3.8 M-' at 299 K . Above a concentration of approximately 0.3 M at this temperature, an altogether different mode of self-ordering sets i n . The multiplicity of H - 8 resonances in the ' H N M R spectra and that of phosphate resonances in the 3 ' P N M R spectra are consistent with the coexistence of two kinds of ordered structures, likely to be octamers and hexadecaniers, respectively. 23%achemical shifts and line widths are also concentration dependent: below a critical concentration, they increase normally with the fraction of ion-paired sodium, just as in model systems (5'-AMP, 5'-ATP, 2'-GMP, D-ribose 5-phosphate). with binding constants of about 2 M-', at 3 0 0 K . Above a critical concentration. the 23T\;aresonance undergoes a pronounced upfield shift, together with a considerable line broadening: these are diagnostic of a sharp disorder-order transition. wjhich can be studied either by changing the concentration at constant temperature, or by varying the temperature at constant concentration. This disorder-order transition is highly cooperative, with a Hill coefficient of 6.1 0.7. From the critical concentrations. determined either from the 23Nachemical shifts or from line widths reduced to unit viscosity, a phenonienologiciil phase-separation model yields AH" = -17 & 2 kcalemol-I and AS" = -51 & 6 cal.mol-'.K-'. The self-assembly is enthalpy driven. rather than determined predominantly by hydrophobic forces, like the normal stacking interactions. The binding of N a + contributes directly to the buildup of octamers and hexadecamers from hydrogen-bonded tetramers whose central cavity includes a sodium cation.
*
Introduction Alone among the nucleotides, guanosine monophosphate ( G M P ) arranges itself into highly ordered aggregates, in aqueous solutions.' The 5' isomer (5'-GMP) not only forms gels at acidic ~ H s , ' but - ~ also self-orders at neutral and slightly basic pH. This phenomenon was discovered in 1972 by Miles and Frazier,6 using infrared spectroscopy. Further X-ray' and I R studies provided nearly conclusive evidence for a planar tetrameric arrangement of G M P molecules held together by eight hydrogen bonds. ' H N M R studies reported in 1975 the high rigidity of 5'-GMP aggregates a t neutral pH: energy barriers of more than 1 5 kcalsmol-I prevent fast exchange of monomer nucleotides between sites.x Two groups then independently discovered by N MR that the self-assembly process depends critically on the cation present: Pinnavaia et aLYusing 0002-7863/80/ 1502-1 I24$Ol .00/0
' H N M R and Laszlo et al.""' using 2'Na and 3yK N M R showed a potassium-selective interaction of alkali metal cations with the central cavity delimited in the tetramers by the four 0 6 oxygens. 5'-GMP aggregation is related to the exceptionally high rigidity displayed by poly(riboguany1ic acid) [poly(G)] in neutral aqueous solution,IJ- I' due to multistrand formation,Ix with a four-stranded form characterized by X-ray in the solid, I9 -20 The self-ordering of 5'-GMP could have had prebiotic significance: nucleotide formation has been documented under abiotic conditions,*[->' and 5'-GMP self-assembles at the slightly basic pHs (7.8-8.4) characteristic of the present and plausibly also of the primeval ~ c e a n . lWe ~ - have ~ ~ indeed already shown2' that 5'-GMP aggregates discriminate between 1980 American Chemical Societ)
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measured at different temperatures, from 0 to 50 OC, and at various concentrations with a Desreux-Bischoff viscosimeter4’ for a reduced volume (2 mL) thermostated to within f 0 . l OC. Densities aredetermined with a pycnometer brought to the same temperature in the thermostated bath. Both the viscosimeter and the pycnometer are calibrated with pure water at different temperatures, using values for the densities and the viscosities from standard sources.48The standard deviation on the flow times (at least five measurements are averaged) is less than 0.25%. However, in order to decrease the time required for viscosity measurements, we have often used another procedure: the viscosity (q) of a solution is measured a t different temperatures, and then at different concentrations. By interpolation on the resulting plot, we determine q as a function of nucleotide concentration at the different temperatures with an uncertainty of f 1%. Measurement of NMR Chemical Shifts and Relaxation Times. 4. ‘ H N M R spectra are obtained with a Bruker HFX-90 spectrometer equipped with Fourier transform, at 90 MHz, with a deuterium lock for field stabilization. Samples are maintained at 22 f I OC. DzO is used as the solvent, providing the internal lock; the residual HOD line, of weak intensity. overlaps little with the nucleotide resonances. Line widths are measured a t half-height (vI/l), and the line width of the inert I ,4-dioxane internal reference is subtracted in order to minimize the effect of inhomogeneous magnetic fields and the changes in viscosity of the solutions with the nucleotide concentration. The chemical 0 shifts are also measured with respect to this same internal reference. Continuous wave ‘ H N M R spectra were recorded on a 250-MHz Cameca spectrometer. ‘ H chemical shifts a r e reported in parts per million with respect to a ,VeaSi external reference, without bulk susceptibility corrections. Temperature control equipment was used in all experiments: temperatures were determined by measuring the chemical shift between the peaks in a methanol spectrum. B. Sodium-23 N M R spectra are obtained at 21.16,23.81, and 62.86 M H z with Bruker WP-80 (Likge), Bruker HFX-90 (Li?ge), and Cameca 250 (Orsay) spectrometers, all in the Fourier transform ( F T ) mode. Samples are introduced in the probe at least 20 min before recording the spectrum, in order to equilibrate to the probe temperature. Measurements are performed in the 0-50 OC temperature range. OH 6 H Temperature in the probe of the Bruker HFX-90 instrument is measured with a thermocouple and a micro-voltmeter: it is measured with a thermometer in the probes of the Cameca 250 and Bruker WP-80 Experimental Section instruments. Owing to the phenomenon studied, with a pronounced temperature dependence of the line width (up to 15 Hz per degree), Preparation of Solutions. Sodium salts of the nucleotides 2‘- and it is indeed extremely important that spectra on different instruments 5’-GMP, 5’-AMP, and 5’-ATP and of D-ribose 5-phosphate are of the best commercial grade (Sigma Chemicals). These are hydrated dibe recorded not only on identical samples, but also at a closely similar sodium salts, of known water content. Knowledge of the sodium temperatures. The line widths are reproducible and accurate within f5%. For NaCl solutions 0.5 M in DlO and HlO, the Z3Naline width content being fundamental for the 23NaN M R measurements, we have checked the sodium composition using flame spectrometry, and we is directly proportional to the measured viscosity, at a given temperhave determined the number of hydration molecules by the Karl ature: u1/2 = 179.9qT-’ 0.777 ( p = 0.996 for 16 experimental Fischer amperometric method. We thus obtain a hydration number points, 8 in D2O and 8 in HzO). The transverse relaxation times 7 2 matching the label within f 15% and a sodium composition of 2 f 0.03 are obtained from the line widths of Lorentzian lines compared to ihose of the NaCl reference: 7rAu112= I / Tz. At constant temperature. sodium atoms per molecule of nucleotide. Solutions are made voluthe reference line width does not change by more than f l Hz with the metrically in DzO (Merck “Uvasol” 99.8%) or in twice-distilled water. field homogeneity. With non-Lorentzian lines, the fast and slow reOnly a t high concentrations of 5’-GMP, N a l ( > O S M), homogenization of the solution requires time (-12 h) because of the high vislaxation components Tz‘ and 7 2 “ are obtained by deconvolution of the composite absorption according to a procedure published elsecosity. The pH of solutions is measured, both before and after recording N M R spectra. with a Tacussel TS 4 I\! p H meter. The pH where.I3 The longitudinal relaxation times T I are measured nith the meter is calibrated with standard buffers (Merck Titrisol), and I8O0-r-9O0 pulse sequence, at different t values.a9 The time variation of the line intensity follows the relationship: In ( I , - I , ) = - r , T measurements are accurate to f O . O 1 pH unit. The pD of the D2O solutions is obtained from the following approximate r e l a t i ~ n s h i p : ~ ~ In ( k l - ) . A linear regression yields T I with a value for the constant k = 1.8 f 0.2, and an uncertainty of f 10%. pD = pH 0.4. Solutions used for the 2 3 h a measurements contain only the disodium salt of the nucleotide and the solvent. These soluC. Durations of the exciting 90’ pulses are 8.5 ps (Bruker WP-80) tions are not buffered to avoid undesirable competition between varand 9 ps (Bruker HFX-90 and Cameca 250). The usual spectral ious anions and cations which would then coexist. .4s a consequence, windows are 6 or 12 kHz. Taking into account the line widths studied. the pH of these solutions varies slightly with concentrations: for exalways below 1 kHz in this study, the spectral distortion is negligible.”’ ample, for 5’-GMP, Na2 it varies by 0.5 pH unit over the 5 X 10-3-1 For a rather typical sample, with a line width at half-height Au,‘ 2 IO0 H7 at 23.81 MHz, the number of scans is 2000 (4K); the same M concentration range. Solutions prepared for ‘ H N M R chemicalshift measurements contain, in addition to 5’-GMP, N a l a n d D2OO.2 sample, with a line width at half-height Aul 12 60 Hz at 62.86 M Hz M NaCI, I ,4-dioxane (Merck “for analysis” I 0-3 M) as an internal requires 500 scans (XK). The S / N ratio for all of the absorptions is better than 40:l. Chemical shifts are measured with respect to a 3 44 reference both for chemical shifts and line width^,^^.^' and EDTA M ) to complex paramagnetic im(Merck “for analysis”, 2 X b a C I in water external reference, extrapolated to infinite dilution in DlO or H2O; since the solutions studied are also aqueous, no susceppurities that might affect the line widths and proton chemical shifts.4h The pH of these solutions is adjusted to the desired value using very tibility correction is made; the attendant error is negligible with respect small amounts of concentrated DCI or N a O D . For relative intensity to the experimental uncertainty.” 5 3 measurements, IH N M R spectra are obtained for solutions of 5’D. 3 ’ P spectra have been recorded in the FT mode: on the Bruker G M P . Na2 twice lyophilized from >99.75% D2O. WP-80 spectromcter (Likge) at 32.37 MHz-I 2-ps 90’ pulses; Viscosity Measurements. Viscosities of the aqueous solutions are 1000-Hz spectral window: line widths of about 10-30 Hz include the
the two a r c h a i ~ * ~ .amino * ~ - ~acids ~ glycine and alanine. And such interactions with amino acids may have a bearing on the origin of the genetic Cation binding determines the self-assembly of the 5‘-GMP dianion. Our investigation focuses on the binding modes of alkali metal cations, site binding or atmospheric condensation; on their binding sites, a t the central cavity of the tetramers or on the doubly charged phosphate groups; and on the thermodynamics and microdynamics of binding and release of univalent cations by the self-ordered structures. These questions are answered using a combination of IH, I3C, and 3 1 P NMR, and the corresponding heteronuclear Overhauser effects, together with direct examination of alkali metal nuclear magnetic r e s o n a n ~ e . ~ ~ ~ ~ ‘ T h e first article is devoted to an examination of the selfassembly of the sodium salt of guanylic acid, i.e., 5’-GMP. In the accompanying article,42we describe results obtained in the presence of other cations besides sodium, especially K + and N H4+, The structure of 5’-GMP and numbering of the atoms are as shown.
+
+
+
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-
1126
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Journal of the American Chemical Society
I
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0.1
0.2
I
0.3
I
1
1
0.4
0.5
0.6
102:3
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I
[5‘GMP] M
Figure 1. Variation of the chemical shift ( 0 )and of the line width ( X ) for the H- I ’ and H-8 protons as a function of 5’-GMP concentration at pH 7.5 and 22 O C . The inset displays the changes in the chemical shifts for the component resonances into which H-8 splits above a critical concentration of ca. 0.3 M (note the difference in scale).
5
10
A 6 (HzI
Figure 2. Plots us_ed for the derivation of the mean self-association equilibrium constant K , for 5’-GMPconcentrations below 0.2 M at pH 7.5 and 22 O C .
units within the clusters. Proton and carbon chemical shifts map the nearest neighbor relationships; because of the ring currents present in purine and in pyrimidine bases, whose effects have been c o m p ~ t e d , local ~ ~ -structures ~~ could be drawn in a number of cases. Self-association of pyrimidine derivativeshl is weaker than for purine derivatives,66 and ring currents in the former63,64,67 do not induce chemical shifts of substantial magnitude. Hence, more is known about adenine derivat i v e ~ . ~ The ~ - upfield ~ ~ , ~chemical ~ - ~ ~shifts of H-l’, H-2, and H-8 upon stacking of adenosine 5’-monophosphate, together with proton relaxation times70 and paramagnetic line broadening in the presence of Mn(II),69 were used to specify welldefined geometries in the dimers. However, 5’-AMP and other adenine derivatives self-associate past the dimer stage and form indefinite stacks.62,68-76 We have followed the proton chemical shifts of the H-I’ and Results H-8 protons of 5’-GMP as a function of on cent ration;^' very similar upfield shifts occur at pH 5,6.5, and 7.5. At the latter Self-Association at Low Concentrations. Base stacking is pH, where gels do not form, the H- 1’ and H-8 resonances shift the normal mode of self-association in aqueous solution for upfield in a normal manner up to a critical concentration of ca. nucleic acid bases, for nucleosides, and for nucleotides: numerous studies have vouched for this p r o p ~ s i t i o n Ther. ~ ~ ~ ~ ~0.3 M (Figure I ) . Then, the line widths increase markedly and split into several components (Figure I ) ; a modynamic parameters are accessible through o s m ~ m e t r y ~ ~the - ~ resonances ~ and calorimetry,60 ~ f t e n ~ ’under - ~ ~ the isodesmic approxidifferent process sets in. It was first reported at a pH close to mation of equal equilibrium constants in the successive equineutrality by Pinnavaia, Miles, and Becker.8 libria B,- I B G B,. Values of A H ” range between -2 and W e analyze the variations in the H-I’ and H-8 chemical shifts a t concentrations below 0.2 M using a standard treat-8 kcal-mol-’, while ASo values vary between -7 and -20 ment;76 in addition to the isodesmic hypothesis, it makes the cal.mol-1.K-’.57~59 Hydrophobic effects have been implireasonable assumption that the chemical shift is determined cated;6’ however, they are not the sole determinants for the predominantly by nearest neighbor molecules i n the stacked i n t e r a c t i ~ n .Because ~ ~ . ~ ~ of the relatively high concentrations array. If Bo is the total concentration and B the free monomer a t which self-association occurs, between and 1 M, nuconcentration, 6~ is the chemical shift for a given proton in the clear magnetic resonance methods could be applied. They have been focused mainly on the geometric disposition of monomer monomer and 6~~ in the dimer, while 6 is the observed chemical coupling to adjoining protons, since these were undecoupled spectra; -500 scans (8 K) are needed for a 40: 1 S / N ratio; on the homemade spectrometer of Professor Gudron (Palaiseau) at I11.7 MHzspectral width = 30 ppm; acquisition time = I .22 s; rate of recurrence = 2.00 s; spectral resolution = 0.8 Hz; >40:1 S / N ratio with 100 scans; Bruker HFX-90 (Paris) at 36.43 MHz-9-ps 90’ pulses; spectral width = 30 ppm; line widths of 10-20 H z lead to 400 scans ( 4 K ) needed for a 30:l S / N ratio. Temperature control equipment was used in all experiments; temperature settings were recorded, but absolute temperatures were not determined. The chemical shifts a r e indicated in parts per million relative to H3P04, 90% as external reference. Proton-decoupled 3 1 PN M R spectra were recorded at I 11.7 MHz, at 281 and 288 K. These temperatures were measured by placing an alcohol thermometer in the probe. All the results are reported with combined uncertainties of f 3 u , i.e., at the >95% confidence level.
+
Laszlo et al. / N M R Studies of 5’-GMP Dianion Self-Assembly
1127
shift; with A6 = 6 - 6 ~then: ,
(Ab/Bo)’/’ = ( K / ~ A ~ B ~ ) ’ / ~-( A6) ~ A ~ B , (1) Hence, a plot of ( A ~ / B o ) ’against /~ A6 (Figure 2) yields from the slope and the ordinate the values of the mean equilibrium constant for self-association K,together with the value of the dimerization chemical shift A ~ BThe ~ . H-8 resonance yields = 3.8 f 0.5 M-l and = 0.09 f 0.02 ppm. The corresponding values from H-I’ are 3.3 f 0.5 M-l and 0.09 f 0.02 ppm, in good agreement. The value of the equilibrium constant = 3.5 f 0.5 M-’ is commensurate with those reported for self-association in a number of cases: purine = 2.1 M-1;54,76adenosine = 4.5-15 M-l;54.66 5’-AMP = 1.7 M-l;78 A T P = 1.3-5.1 M-l.66.73 Using the above value of E, we calculate the distribution of 5’-GMP between monomers, dimers, trimers, etc., for various total concentrations in 5‘-GMP.77 At M, the monomer predominates to the extent of 94%; only 6% of dimer is present. At 0.2 M, 5’-GMP still exists predominantly as the monomer (46%), coexisting with the dimer (30%). On the basis of this simplified model, in which 5‘-GMP molecules interact only by the stacking of monomeric units, it is only above a concentration of -I M that the percentage of dimers plus trimers overtakes that of monomers. However, it is clear that above a critical concentration, ca. 0.3 M at 22 OC, an altogether different mode of self-ordering occurs, leading to a different type of aggregation than normal base stacking. Ion Pairing of Na+ with Nucleotides. We shall examine first the concentration dependence of the 23Nachemical shifts and line widths of several nucleotides capable of “normal” selfassociation. For all these compounds, the extreme narrowing condition is fulfilled so that determination of the line width at half-height u 1 / 2is equivalent to measuring the transverse relaxation rate: R2 = T2-l = 7 r v 1 p ~We O find an increase of u112 with the concentration in D20, between 0 and 0.6 M, of the disodium salts of D-ribose 5-phosphate, adenosine 5’-monophosphate, adenosine 5’-triphosphate, and guanosine 2’monophosphate. Even when the observed line width is divided by the measured bulk viscosity 7,the resulting line widths reduced to 1 m P vlp* are still found to increase with c ~ n c e n t r a t i o n In . ~ ~all these cases, the line width u l p decreases when the temperature increases; there is fast exchange of the N a + cation between the different sites it can occupy.79Then by describing the system as a two-state equilibrium, the observed reduced line widths ul/2* and chemical shifts 6 are given by: ull2* = P F u l / 2 F -k
6 = P F ~ A+ P
pBuI/2B
(2)
B ~ B
(3)
where the letters F and B refer to the free and bound states, respectively. As the concentration of each disodium salt increases, so does the fraction p~ of ion-paired sodium in the equilibrium: RP2-
K
+ N a + 3 RP2- - N a +
(4)
Denoting x as the equilibrium concentration of ion pairs and COas the analytical concentration in disodium salt: p~ = x/ZCo and K , = x/(Co
- x)(2Co
- X)
(5)
it follows that: ( V l / 2 * - VI/2F)/(VI/2B - VI/2F) = x / 2 c o (6) By combining eq 5 and 6, the experimental results for D-ribose 5-phosphate can be analyzed.77 The cases of the nucleotides are more difficult to analyze, because the self-association of the nucleotide is superimposed
Figure 3. Variations of the 23Na reduced line width u ~ p r l - ’ against those of the 23Nachemical shift in solutions of 2’-guanosine monophosphate, disodium salt, a t 20 O C , and for various concentrations.
on the ion pairing described by eq 4. A qualitative comparison of the results will serve as a background for description and analysis of the results for 5’-GMP, which are in an altogether different class. At the higher temperatures (18 and 25 “C), the curves for 5’-AMP and for D-ribose 5-phosphate are very similar: obviously, at these temperatures self-association of the nucleotide is small (corresponding to an equilibrium constant = 2 M-I a t ambient temperature^'^). By contrast, the greater tendency of A T P toward self-association (K in the range 5-50 M-l according to the conditions and methods of s t ~ d y ~ ~ ~ ~ ~as~ a~ much ~ ) s more h o wabrupt s increase of u l p * with concentration a t 5 O C . At the same temperature of 5 O C , the dependence of the reduced 23Na line width for 2’-GMP shows another striking difference: the initially convex curve becomes concave above a concentration of -0.45 M. Interestingly, there is sufficient resemblance between the concentration dependence of the 23Na chemical shift, for the same compound and under the same conditions, that the A u l p * and A6 variations are linearly related to one another (Figure 3). Under fast exchange conditions, such a proportionality indicates, on one hand, the complete absence of line broadening from chemical exchange, and also a common origin for the changes in the line widths and in the chemical shifts. The most reasonable assumption is for both types of parameters to increase with the fraction p~ of ion-paired sodium: a t this temperature of 20 OC (Figure 3) self-association of 2‘-GMP has a negligible influence on the sodium line width. Analyzing the chemical-shift variation in terms of equilibrium 4, and using eq 7, which is the counterpart of eq 6:
(6 - J A ) / ( ~ B- JA) = ~ / 2 C o (7) we find a K, value for 2’-GMP at 20 O C of 1.5 f 0.4 M-I, commensurate with the stability constant of 2.2 f 0.2 M-’ determined a t 25 OC using p H measurements and a t an ionic strength of 0.2 for the Na+-5’-AMP2- ion pair.82 As for the variation A6 of the 23Nachemical shift of bound sodium in the ion pair, as compared to free sodium at infinite dilution in D20, it is equal to 1.3 f 0.3 ppm toward lower field. Self-Assembly at Higher Concentrations. Proton N M R and phosphorus-31 N M R can be used to follow 5’-GMP self-assembly. IH N M R spectra (250 M H z ) of a 0.7 M solution of the sodium salt of 5’-GMP i n D2O were obtained in the temperature range 273-307 K. They agree with those published previously.* The spectra (H-8 region) obtained at 273 and 307 K are shown (Figure 4) with the labeling of H-8 peaks to be used. Deconvolution of the H-8 region of the proton spectra obtained in the range 273-307 K yielded the relative populations of Table I and the chemical shifts shown in Figure 5 .
Journal of the American Chemical Society / 102.3
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January 30, I980
40t 307 K
Figure 4. H-8 region of 250-MHz IH N M R spectra of a 0.7 M solution of 5'-GMP, Naz in D20 at 273 and 307 K. These spectra show the labeling of peaks in the H-8 region used in the text. 01
\
I
I
273
7'.I
200
290
300
3t0 K
Figure 6. Temperature dependence of the relative populations of the peaks in the 36.44-MHz 3 ' P N M R spectra. Other conditions are as in Figures 3 and 4: (m)low-field peak; (v)high-field peak.
- --
/*--
Y 'I
HL)
80
6.1
-
H.3 0
1
e80'
5.1
l
27'3
I
I
200
290
300
307 K
40
IC0
Figure 5. Temperature dependence of the chemical shifts, in parts per million from a MerSi-containing capillary, for H-8 region resonances in 250-MHz ' H NMR spectra; other conditions are as in Figure 3: ( 0 ) cy peak; ( X ) /3 peak; ( + ) y peak; ( 0 )6 peak; ( * ) x peak. 20
3 1 PN M R spectra were also recorded a t 36.44 MHz for the same samples under identical conditions. A single phosphorus resonance is seen at the highest temperature examined, ca. 307 K. As the temperature is lowered, however, a second peak appears about 2.2 ppm upfield from the original resonance. The relative positions of these two peaks did not change with temperature, down to the lowest temperature examined (273 K). The relative weights of the two phosphorus resonances are plotted as a function of temperature settings in Figure 6. Comparison of Figure 6 with the data of Table I shows that the temperature behavior of the high-field 3 1 Presonance mirrors that of the a and 6 I H resonances. Proton decoupling did not affect the relative populations of the two phosphorus resonances observed at 36.44 MHz. Of these two resonances observed a t 36.44 MHz, the lowfield component is resolved into two peaks at higher field. Three phosphorus resonances are in fact observed a t 1 1 1.7 MHz for
200
L so T
'C
Figure 7. 23Naline width u l i 2 and chemical shift Ad as functions of temperature for solutions of disodium salts of 5'-guanosine monophosphate (0.45 M) and of 2'-guanosine monophosphate (0.45 M ) in 1 1 2 0 and H 2 0 solution.
an 0.8 M solution of 5'-GMP, Naz in D 2 0 at 28 1 and 288 K.I2 Deconvolution of these two 1 1 1.7-MHz 3 1 PN M R spectra shows equality of the populations of the highest and lowest field "P peaks at both temperatures investigated. These two peaks
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Table I. Temperature Dependence of the Relative Populations of Peaks in the H-8 Region of 250-MHz Spectra of a 0.7 M Solution of 5'-GMP, Naz, in D20 T. K
peaks
273
CY
27 31 15 27
P Y 6
a
282
298
307
23
13 730
90
14
5
26
5
27
24
x peak (see Figure 3).
Table 11. Critical Concentrations (CCI, See Text) Determined from Line Widths Reduced to Unit Viscosity (a) and from Chemical Shifts (b) T, K
solvent
CCI, M
273 273 278 278 278 288
D2O D2O D2O D2O
0.12 f 0.029 0.134 0.015b 0.15 f 0.029 0.16 f 0.02b 0.17 f 0.02d 0.27 f 0.04a 0.29 f 0.03b 0.30 f 0.05" 0.34 f 0.04a 0.38 f 0.04b 0.43 f 0.06a 0.53 k O.Ogb 0.45 f 0.06a 0.70 f 0.1 5a 0.70 f O . l O a
I
288 288 293 293 300 300 300 310 310
H2O
D2O D2O H2O
D20 D2
0
DzO D20 H20
D2O H2O
5OC
" I
*
-
0
A\ 't n I
u
20°C
-
"
-0
are separated by 2.3 ppm a t 281 and 288 K. The central 31P resonance appears -0.15 upfield from the lowest field 31Ppeak a t both these temperatures. Self-Assembly: Phenomenological Approach. Sodium-23 nuclear magnetic resonance40 is a choice method for studying 27"c 7 binding of the sodium cation with biomolecules in aqueous -0 solution. Binding of even a few percent of the N a + ions to a QQ2: , . 37OC ,. 1 1 Y 7 1 slowly reorienting macromolecule or molecular assembly will 0 0 1 0 20 30 40 show up through an enhancement of the quadrupolar relaxa[5' OMPI-' M-' tion rate; attachment of Na+ ions to antibiotic ionophore^,^^-*^ cation binding protein^,^^,^^ synthetics8 or natura141~8y-y1 Figure 8. 23Na-reduced line widths u l I 2 q - l as a function of reciprocal 5'-GMP concentration in D20 solution, at various temperatures. polyelectrolytes, and nucleic acid^^*-^^ has been studied in this manner. 23Na N M R chemical shifts and line widths are measured as a function of 5'-GMP concentration and temperature, in upon self-assembly is to plot them as a function of reciprocal HzO or D 2 0 solution.77 By plotting these parameters as a nucleotide c o n c e n t r a t i ~ n(Figures ~ ~ , ~ ~ 8 and 9). No significant function of temperature, at constant nucleotide concentration solvent isotope effect (H20-DzO) is seen on either of these one obtains sigmoidal curves (Figure 7 ) , highly reminiscent ob~ervables.~~ of the melting curves reported in the literature for the aggreAt each temperature, the chemical-shift variation is seen gates formed in aqueous solution by guanylic acid at pH 8, to consist of two straight lines with a sharp intersection: the either from proton N M R or from infrared data.6%8 By contrast, chemical shift remains approximately constant up to a critical no transition is observed with another nucleotide, 2'-GMP concentration, where it drops to strongly negative values (Figure 7 ) . Comparison between these sodium-23 results and (Figure 9). Correspondingly, the line widths are also invariant the proton N M R results displayed earlier (Figure 1 ) shows that u p to the same critical concentration as the chemical shifts, both spectroscopies are sensitive to the same phenomenon, an where they increase abruptly until a maximum is reached a t order-disorder transition as the temperature is raised. If, a second critical concentration (Figure 8). We shall denote CC I and CC2 these two critical concentrations. We shall be conversely, the temperature is kept constant, increasing the nucleotide concentration leads to: (a) splitting of the H-8 examining the significance of CCI and CC2 in a later section. The critical concentrations CCI are listed in Table 11. There proton resonance into several lines, whose widths are augmented; (b) a pronounced upfield shift of the 23Naresonance is very good agreement, within the combined uncertainties, between the critical concentrations determined from the line for the N a + counterions; (c) a considerable increase in the line widths for these sodium ions. widths and from the chemical shifts. Before exploiting the latter parameter, we normalize line Deeper insight into the self-assembly process, and sodium widths to unit viscosity using the measured viscosities for the binding, is afforded by analysis of the 23NaN M R line shapes, s ~ l u t i o n . ~A' convenient representation of the changes of the a t concentrations above CCI, in the 273-300 K temperature 13Na normalized line widths Avl,z-' and chemical shifts A6 range. The 23Na absorption for N a + exchanging between the A
v
m
A
-
Journal of the American Chemical Society
1 I30 [5'GMP]"
-
0
10
20
I
I
e-
M-'
30 I
40 37ac
~
'-
- 0
/
102.3
1 January 30, 1980
Scheme I. Self-Assembly of the 5'-Guanosine Monophosphate Dianion in NeutLal Aqueous Solution in the Presence of Sodium Cations regular, ordered structure a
peak,
6
peak
a relatively stable form containing two
different b u t equally populated types of 'H-8 a n d 31P environments.
Y
regular, ordered structure 5 peak
/
peak
time-averaging o f two or more classes o f 'H-8 protons a n d 31P nuclei in rapid chemical
a form containing a single type of 'H-8 a n d 31P
environment.
tl ? I
d
,.
Oi
n
- 0
AS
T
I
10°nz
I
Figure 9. Variation of the 23Nachemical shift as a function of reciprocal 5'4 MP concentration in D20 solution, at various temperatures.
free state in aqueous solution and the bound state on a slowly reorienting macromolecule is the superposition of two Lorentzians, corresponding to a fast relaxation (60% of the total intensity) and a slow relaxation (40% of the total intensity). Separation of these two components is achieved by full digital deconvolution of the experimental line shape.13 One thus obtains the values for the product p ~ x where ~ , p~ is the mole fraction of sodium ions in the bound state and x is their quadrupolar coupling constant, together with 7,, the correlation time for these bound sodium ions (Table HI).In order to check the accuracy of this analysis, we have run a series of spectra for the same samples a t 62.86 MHz. Given the orders of magnitude for thepBx2 and the T~ terms in Table 111, it is predicted from the appropriate equationsI3 that only the slow relaxation rate component should be visible a t this higher frequency. This is indeed the case. Whereas a t 23.81 M H z the observed sodium line is distinctly non-Lorentzian, consisting of the superposition of two Lorentzian lines with differing widths, at 62.86 M H z only the narrow component (40% of the total intensity) can be seen. Furthermore, the relaxation rates 1/ T ~ Bmeasured " a t the higher frequency agree well with those calculated from thepeX2 and T~ values obtained a t the lower frequency (Table 111).
Comparing the third and the penultimate column, 7, does not follow the bulk viscosity 17, even though 17 changes by more than 300% between the less and the more viscous solutions. This already suggests that the measured correlation time T , cannot be identified with the reorientational correlation time T R for the aggregates. If one assumes that the species formed in the sole presence of sodium ions and the potassium-containing aggregates42have comparable aggregation numbers and similar structures, then the 7 R values of 9.4 f 1 ns obtained for the (Gs, K', nNa+) species42 translate into 7 R values of 16 ns a t 25 mP, 25 ns at 40 mP, 38 ns a t 60 mP, and 50 ns a t 80 mP. The correlation times T, listed in Table 111do not follow uiscosity, and they are significantly smaller than the values expected for the reorientation of a (G8, Na+, nNa+) species. The inference is that the correlation times 7, are predominantly determined by the residence time 7 8 of the sodium ions on the aggregates. With 7,-' = 7R-I 7 B - ' , 9 6 the resulting 7 B values are also indicated in Table 111. Because of accumulated errors, only an order-of-magnitude estimate is obtained; N a + cations stay on the aggregate for approximately 30 ns.
+
Discussion A conspicuous feature of the aggregates formed by 5'-GMP, N a l is the coexistence in the ' H N M R or in the 3 ' P N M R spectra of three singlet resonances: two minor outer resonances and a major inner r e s ~ n a n c e . ' ~W , ' ~e have measured their relative intensity ratio R a t different temperatures in the 3 ' P spectra (Table IV). It is readily apparent that thepBX2 values, obtained by the deconvolution of the experimental 23Na line shapes, follow a similar trend (Table IV). The correlation between the two sets of parameters is very good, with a correlation coefficient of 0.984 for five points. The temperature dependence of R corresponds to AH = - 17 f 2 kcal-mol-' and to AS = -63 f 6 cal.mol-'.K-'. Likewise, ' H and 3 1 Presults are interrelated: joint consideration of the two kinds of spectra suggests that the lowest field and the highest field 3 1 Presonances correspond to phosphorus-3 1 nuclei belonging to the same chemical species as the lowest field ( e )and the highest field ( 6 ) H-8 protons, respectively. This chemical species has a regular, ordered structure. The central 3 ' Ppeak in like manner corresponds to the p and y 'H-8 resonances. In Scheme I, we thus extend to the phosphorus-31 resonances the same labeling used for the H-8 proton resonances: lowest field 3 1 p peak = a;central 3 ' P resonance = p,y; highest field 3 ' P peak = 6. This scheme outlines one of the simplest possible interpretations of the ) ' P and 'H-8 N M R data (this description has been hinted a t in the litera-
Laszlo et al.
/ N M R Studies of 5‘-GMP Dianion Self-Assembly
Table 111. Values of p b x 2 ( f l 5 % ) , of
T~
(f15%), and of
T B for
1131
a Series of Samples at Various Temperatures“
[5’-GMP2-, Na2+], M
T, K
7, m P
I/Tzs’, HZ
I/Tze”, HZ
PBX’, 10’’ HZ2
T ~ ns ,
7 8 ,ns
0.152 0.203 0.324 0.370 0.450 0.600 0.896 0.152 0.203 0.324 0.370 0.450 0.600 0.744 0.896 I .oo 0.324 0.450 0.600 0.744 0.896 I .oo 0.450 0.600 0.744 0.896
273 273 273 273 273 273 273 278 278 278 278 278 278 278 278 278 288 288 288 288 288 288 293 293 293 293 293 300 300 300 300 300 300
30.0 32.5 40.0 43.5 51.0 75.0 b 25.0 27.0 34.0 36.5 42.0 58.0 80.0 b b 24.0 30.0 41.0 56.0 b b 26.0 35.0 48.0 b b 30.0 40.0 41.0 45.0 b b
2 810 2 080 6 800 7 460 10 500 9 920 9 200 468 2 780 9 940 7 990 7 910 7 280 8 460 6 670 6 510 1870 6 780 11 900 12 800 9 720 9 560 1930 6 270 6 940 9 200 6 360 3 080 3 340 4 840 8 120 8 940 ( 15 000)
573 1060 I700 I750 1870 1830 I620 20 1 704 I730 1750 I750 1690 1660 1450 1390 64 1 1570 1800 1820 1620 I490 820 1410 1590
7.87 10.5 22.5 23.9 29.3 28.7 25.4 1.66 9.01 27.5 24.8 24.7 23.3 24.9 20.6 19.9 7.26 21.8 30.9 32.2 26.9 25.1 8.72 19.9 22.3 25.8 20.3 10.6 13.6 16.0 22.8 24.5 33.8
15.1 (6.3) 12.3 12.9 15.7 15.3 15.8 9.2 12.5 15.8 13.6 13.4 13.0 14.6 13.6 13.8 9.6 12.9 17.2 17.9 15.9 16.9 7.7 13.2 13.0 15.6 13.1 11.6 9.1 12.4 15.6 16.0 20.4
75 f 40
1 .oo
0.600 0.744 0.753 0.800 0.896 1 .oo
a
1810
1440 825 1 I80 1 I80 1430 1500 (1 700)
The fast and slow relaxation rates ( & I O % ) are also indicated. The Larmor frequency is 23.81 MHz.
Table IV. Intensity Ratio R (Sum of Outer Peaks vs. Central Peak (0.7 M ) as a Function of Intensity) and PBX’ for 5’-GMP2-, Temperature
T, K
R
10’’ Hz2
T,K
R
PBX2, 10’’ Hz2
275 280 285
0.37 0.36 0.30
16.2 15.7 13.7
290 295
0.22 0.16
12.8 10.9
PBX2,
tures) for the 5’-GMP, Na2 system. It appears to fit well the 3 1 Pand ’H-8 chemical shifts, line widths, and relative populations. Scheme I is characterized by the coexistence of species with small values of their reorientational correlation time 7c (y peak), and of ordered structures with long 7c values ( p peak and a,6 peaks). The sodium-23 N M R results indeed can be analyzed quite accurately in terms of the coexistence of a fast reorienting and of slow reorienting bound states, which agrees with the characteristic appearance of the plots in Figures 8 and 9 and with the finding of a critical concentration CCI. Using a simplifying two-state, phase separation model, the standard free energy AGO of self-assembly is given by:97398
AGO = R T [ 1
+ ( m / n ) ]In (CCI)
(8) where m is the number of counterions Na+ and n is the number of nucleotide units within the aggregate, so that m/n is the fraction of charge neutralized for each monomer unit within the n-meric aggregate. The term [ l (m/n)] varies between 1 and 2 according to the degree of ionization of the monomers i n the aggregates. We have chosen a value of 5 / 16 for the m/n ratio, for reasons that will be apparent from the later sections. Also, the system is far from being ideal at the critical concen-
+
2 5 f 15 2 5 f 15 3 0 5 15 25 f 15 2 0 f 10 50 f 25 60 f 30 35 f 20 3 0 f 15 2 0 f IO 20% IO 2 5 % 15 40 f 20 50 f 25 40 f 20 15% 7 35 f 20 2 5 % 15
3 0 f 15 1 5 1 7 2 5 f 15 35 f 20
Not determined.
trations of Table 11; therefore, we determine thermodynamic parameters from eq 9, in which activities replace concentrations:
AGO = 1 . 3 1 R T I n a
(9)
W e obtain these activities a by multiplying the CCI values from Table I by the activity coefficientsf calculated from the ionic strength I with the Davies formula99(eq 10):
The ionic strength, taken as I = (I/2)ZcLz,*,is probably a slight underestimate because of the high charge of the aggregates, which, on the other hand, have very low concentrations a t the critical concentration. This phenomenological treatment works nicely; the In a values are indeed linear with reciprocal temperature as implied by eq 9 (correlation coefficient = 0.993 for five points), yielding the following thermodynamic parameters: AH” = - 17 f 2 kcal-mol-’ and A S o = -51 f 6 cal.mol-l.K-l. These values are very slightly a t variance from those reported in a preliminary communicationlo and which were obtained from the use of eq 8 instead of the more correct eq 9. There is excellent apparent agreement between these values, obtained from the chemical shifts and relaxation rates for the N a + counterions, and those determined by the completely different route of intensity ratios from 3 ’ Pspectra for the 5’GMP2- dianion. However, this could also be an accidental coincidence, with the different methods looking at distinct phenomena, a point which we now examine.
1132
Journal of the American Chemical Society
By analogy with the potassium-containing system,42 and because of the similarity of the 23Na correlation times, octamers Gg appear reasonable as the predominant aggregates. A first possibility is that, at a rather high 5'-GMP concentration of 0.7 M (that of Figures 3 and 5 and Table IV), the CY 6 peaks correspond to octamers, while the central p peak corresponds to tetramers. The correlation obtained with p ~ (Table IV) implies greater binding (or condensation) of the sodium cations upon the octamers. While such conclusions are qualitatively plausible, we were unable to effect a quantitative analysis using this sole model. The second interpretation, which we tend to favor, is that the two types of measurements "see" different processes, albeit characterized by very similar parameters; the phenomenological approach of critical concentrations (23Na results) describes predominantly the 2G4 2 G Xequilibrium, while the intensity ratio measured at 0.7 M ( 3 ' Presults) refers to another equilibrium, the dimerization of two Gg units into a hexadecamer: 2Gx e (316. The Gg species can exist in conformations with C4h or S S symmetry, leading to observation of a single resonance for either the H-8 proton or the 3 1 Pnucleus in the phosphate group ( p peak). Dimerization of G8 into a hexadecamer may lead to a species with effective twofold symmetry: simple stacking of tetramers will result in two "inner" and two "outer" tetramers, with 1:l ratio ( a 6 peak). Alternatively, if a sodium cation sandwiched in between two phosphate groups effects the dimerization of two Gs units into a G16 species, the observed spectra would require fast interconversion between the proximal and the distal positions. Whatever the structures present, it is reasonable to assume that, to a good approximation, all the 5'-GMP molecules are aggregated a t this rather high 0.7 M concentration. Furthermore, in a similar way as Gg binds N a + cations more than Gq, because of the bringing together of negatively charged phosphate groups, the Glh species would display increased sodium binding for a similar reason, thus accounting for the p ~ variations x ~ listed in Table IV. A third interpretation should be mentioned: the ( a 6) and the p peaks all correspond to octameric G8 structures; indeed, it is possible to group the various Gg conformers in two distinct manifolds: the stacking of planar tetramers occurring either face-to-face, leading to a single (p) resonance, or face-to-back, in which case diastereotopic a and 6 resonances can be expected, at least for certain conformations. The first two interpretations we have just presented agree with one another in ruling out the possibility that the two coexisting species have identical aggregation numbers, differing only in structure. However, it is impossible to check this point directly, since, as noted above, the correlation time T~ is not determined by the reorientational time T R , but by the residence time T B (taking into account the coexistence of Gg, for which T R N 10 ns, together with 10-50% Glh, for which T R N 20 ns, does not affect significantly the values of T B given in Table 111). A simple test will show that the above description is reasonable: by analogy with the ( ( 3 8 , K+, n N a + ) species,42 one may assume that the octamer binds 5 out of the 16 total h a + cations, and that the octamer is indeed, above the critical concentration CC I, the major species. This implies a PBvalue of 5 / 16, above CC 1 at each temperature. In other words, we attribute the small variations with temperature of p B x 2 a t the concentration of 0.7 M (Table IV) to the presence of a small amount of hexadecamers, while the large variations of p B x 2 with concentration a t a given temperature (for instance, it jumps tenfold from 1.66 to ca. 25 at 278 K when the concentration goes from 0.1 5 to above 0.3 M), i n Table 1 1 1 , are due to the G4 G Gg equilibrium. from Using the plateau values for p B x 2 of 25-30 X Table 111, together with p~ = 5/16, yields a quadrupolar coupling constant x = 0.9 f 0.1 MHz. Such values are slightly
+
+
+
1 I02:3 /
January 30, I980
greater than those corresponding to simple phosphate binding of 0.68 f 0.08 MHz, in the (G8, K+, nNa+) species;42this is consistent with occupation of the core position by one sodium cation in the corresponding (G8, Na+, nNa+) species; with n = 4, the core position is characterized by a quadrupolar coupling constant of 1.8 M H z (assuming that the observed x is x the~weighted average between the inner and the outer sites). Such a high value, still in the 0.2-2 M H z range of sodium-23 quadrupolar coupling constants,40 is in good qualitative agreement with the pronounced high-field shift of the 13Na resonance upon aggregation: Kintzinger and LehnIoo have reported such a x-6 correlation in sodium cryptates, in line with the theory by Deverell.lol Going to the interpretation of the T B data in Table 111, simple ion pair dissociation-recombination, with a binding constant equal to that in the monomers about 2 M-I, would lead from AG* > AG and k - = KT/h exp[-(AG*/RT)] to residence times T B in the nanosecond to picosecond time range, too small by at least one or two orders of magnitude with respect to the experimental. Another possibility would be for exchange to occur whenever a 5'-GMP unit with the N a + cation rigidly ion-paired to it broke away from the oligomer, such as the monomer G n-mer exchange. Then the applicable AGa energy barrier would have to be a t least 15 kcal-mol-' from the chemical-shift differences observed in the H spectrum.8 This would correspond to T B > 1.7 X s, Le., to a completely different process than the relatively fast sodium exchange monitored by 23Na N M R . A better explanation is provided by other features in our data: let us consider as the source for the AGa barrier the AG terms we determine with the phenomenological treatment for sodium-binding cumaggregation. With AH = -17 kcal.mol-' and AS ? -50 cal.mol-l.K-', AGO * -3 kcal-mol-' at 273 K. Taking AGa as the amount at least necessary to overcome this stabilizing energy, say 3 kcal-mol-', leads to 7-8 = 16 ns at 300 K, i.e., to the correct order of magnitude. In short, observation of 7 B 30 ns rules out conclusively sodium binding to a single phosphate, and is consistent only with sodium binding by several groups-perhaps a coalition of.oxygen and nitrogen atoms from phosphate groups, the ribose sugar, and the guanine base are all involved in the formation of these sodium binding sites. This conclusion should be strongly emphasized: sodium cation binding contributes directly to the buildup of octamers and hexadecamers. However, it does not follow from this conclusion that cation release from the aggregates destroys them; whereas sodium cations exchange with rates of IOi-lOx s-l, the nucleotide counterions exchange with much slower rate constants, of less than 1 O2 s - I . A point worthy of remark is the magnitude of the limiting chemical shift of 23Na in the aggregates. The observed chemical shift of 15 ppm is the weighted average between the limiting values for occupancy of the inner sites, of the outer sites, and for free sodium ions in the solution (or atmospherically condensed sodium ions around the aggregates). With various assumptions made about the limiting chemical shift for the peripheral Na+ (-20 or -10 ppm), and for atmospherically condensed sodium ions (shifted upfield by 3-5 ppm by the ring currents of the guanines), one comes up with a limiting chemical shift for N a + in the central position of the tetramers in the range of - 100 to - 160 ppm. There are precedents in the literature for such pronounced changes of the sodium-23 chemical shift with the environment of the sodium ion.'"'Such a value is uniquely consistent with Naf inclusion in the central cavity of the tetramers, and indicates that it coordinates there with atoms of strongly differing types: beside the four 0 - 6 oxygens, O H oxygens or guanine nitrogen appear to be also involved. Correspondingly,'oo.lo'the quadrupolar coupling constant for this central sodium has also a very high value of 1.8 MHz. N-
Laszlo et al.
/ N M R Studies of 5'-GMP Dianion Self-Assembly
True, the use of sodium-23 N M R suffers from the disadvantage that the N a + cations exchange fast between several binding sites, as well as with the unbound or atmospherically condensed ions. Despite this limitation, it is a very useful adjunct to the N M R of covalently bound nuclei such as IH and 31P: it provides direct information about the local environment of the N a + ions in the bound sites. From the large magnitudes of the limiting chemical shift and quadrupolar coupling constant, we have inferred occupancy of the central cavity of the tetramers by sodium cations. In addition, 23Na N M R provides values of the correlation times T , for bound sodium ions. By using an attribution for the ordered structures that is strongly suggested by the ' H and 31Pevidence (Scheme I), and by analogy with the (G8, K+, nNa+) structures formed in the presence of potassium ions,42we could derive values T B for the residence times of N a + ions in the bound state(s). They show that N a + ions are indeed directly involved in the stabilization of G8 and GI6 ordered structures. Our phenomenological analysis of the increase in 23Na N M R relaxation rates above a critical concentration CC1 is made with a two-state model. It lumps together the two kinds of ordered structures, corresponding to the /??peak and to the ( a 6) (Gg and GIG);from the viewpoint of 23Na NMR, these are seen as a single entity characterized by a single value of the limiting relaxation rate, because the corresponding correlation times are very similar, differing (at most) by a factor 2. Despite the simplification inherent in the use of such a phase-separation model, it is firmly based in the precise experimental determination of a critical concentration C C l at each of several temperatures (Figures 8 and 9). Another and altogether different model can be applied successfully to the data, and it leads to very similar conclusions. The order-disorder transition undergone by 5'-GMP has cooperative character, as shown by sigmoidal curves such as in for the term Figure 7. Using a plateau value of 30 X p 8 x 2 (Table III), percentages of saturation (y/( 1 - y ) ) can be determined a t each temperature, in the rising portion of the p ~ x vs. * [Na+] curve. They fit the Hill equation:Io3
+
In (y/( 1 - y ) ) = In K
+ n In [NaC]
( 1 1)
The corresponding parameters are listed in Table V. The resulting Hill coefficient n = 6.1 f 0.7 indicates positive cooperativity for sodium binding to the 5'-GMP aggregates, and its value is nicely consistent with the above model, in which octamers with a total of five binding sites (one inner plus four outer sites) as the major species coexist with hexadecamers with ten binding sites (two inner plus eight outer sites), as the minor species. The equilibrium constant K corresponds to AH = -53 f 5 kcal-mol-' and AS = -180 f 20 cal.mol-'.K-' ( p = 0.992 for AG = AH - T A S a t the four temperatures of Table IV). While the signs of these thermodynamic parameters are of course adequate for a self-ordering process, their values should be compared neither to the thermodynamic parameters obtained from critical concentrations, which monitor the 2G4 F! Gg equilibrium, nor to those obtained from 3 1 Pintensity measurements, which monitor the 2Gg F! G16 equilibrium. We are looking with the Hill formalism a t the overall process of sodium binding to a Gg Gl6 mixture. One may note here that analysis of the melting curves7' exemplified by Figure 7 with the crude equation:Io4 AH
+
(%)Tm
=
4RT,2
yields AH -45 kcal-mol-l, in semiquantitative accord with the result from the Hill plot. A recurring feature in our results is the finding that selfassembly is enthalpy driuen, since the entropy change upon self-association is strongly negative. This is reminiscent of the self-assembly of polynucleotides. Furthermore, this differen-
1133
Table V. Hill Coefficient n and In K as a Function of Temperature for Self-Assembly of 5'-GMP, Na2
278 288
6.86 6.45
5.33 1.70
293 300
5.38 5.57
-0.30 -1.61
tiates the 5'-GMP self-assembly from aggregates of micellar type: we are not dealing here with micelles (despite recourse in an earlier report to a formalism used to describe micellesg5); the formation of micelles is characteristically entropy driven; their monomer concentration remains equal to the critical micelle concentration (cmc) above the cmc; the usual cmc's are smaller by two or three orders of magnitude than the critical concentrations we see. Likewise, the aggregation numbers for typical micelles are of the order of 100,'05-107 Le., markedly greater than those applicable to 5'-GMP self-assembly. The value of the enthalpy change found here for the 2G4 Gg process, viz. -22 to -26 kcal.mol-', is strikingly similar to values characteristic of interactions between tetranucleotides such as - 19 kcal-mol-I for the UUCCUG,AA i r ~ t e r a c t i o n . ' ~There ~ ~ ' ~ is~ a balance between the loss of translational entropy for the nucleotides in the 2G4 e Gg and 2Gg e GI6 equilibria, and the gain of translational entropy for some of the water molecules released by the alkali metal cations as they bind to the aggregates; that sodium cations are only partly dehydrated upon site binding to the aggregates is apparent from the magnitude of the observed quadrupolar coupling constant. However, the observed entropies are strongly negative. This would appear to imply a structuring of solvent molecules about the aggregates. Selfassembly of the 5'-GMP nucleotide does not occur because of the attendant release of numerous water solvent molecules. The D20-H20 solvent isotope effect is below the limit of experimental uncertainty. Self-assembly of 5'-GMP, unlike a normal stacking interaction,6' is not determined predominantly by hydrophobic forces. Cation binding plays the important role, together with and reinforcing the hydrogen bonding of the guanines into planar tetramers.
-
Acknowledgments. This work has benefited from the generosity of Fonds de la Recherche Fondamentale Collective (Brussels) (Contracts 2.4610.72 and 2.4504.78), which provided Bruker spectrometers HFX-90 and WH-80 used in this study. Spectra have also been obtained on high-field spectrometers with the kind hospitality extended us by Professors A . Gaudemer (Orsay), M. Gueron (Palaiseau), and' J . Y. Lallemand (Paris). We also thank Dr. C. Merienne, Dr. J . L. Leroy, and Mr. J . Denoel for their help. Exploratory 3 1 P spectra were obtained through the courtesy of Drs. D. Houalla and R. Wolf (CNRS, Toulouse). Mrs. S. Schoos (Liege) has determined sodium contents using flame spectrometry. One of us (A.P.) gratefully acknowledges predoctoral fellowships from I.R.S.I.A. and FkdCration belge des Femmes dipldmtes des UniversitCs, while M.B. benefited from a postdoctoral fellowship granted by Patrimoine de 1'Universitt de Liege. We are appreciative of the referees' constructive criticism. References and Notes (1) W. Guschlbauer and J. F. Chantot, in Proceedings of the International Conference heid in Dymaczewo near Poznan, 13-17.9.1976, Poznan, pp 96-114. (2) M. Gellert, M. N. Lipsett, andD. R . Davies, Proc. Mat/. Acad. Sci. U.S.A., 48,2013-2018 (1962). (3) R . B. Homer and S. F. Manson, Chem. Commun., 11,332-333 (1966). (4) J. F. Chantot, Arch. Biochem. Biophys., 153, 347-356 (1972). (5) V . Sasisekharan. S. B. Zimmerman, and D. R . Davies, J. Mol. B i d , 92, 171-179 (1975). (6)H. T. Miles and J. Frazier, Biochem. Biophys. Res. Commun., 49, 199-204 (1972).
1134
Journal of'the American Chemical Society
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